Yes, the total mass, but it's hard to imagine the mass emitted at any given second (aside the launch) would be that big. Although, I could imagine they don't need that big forces in space.
As long as you don't try to land or start from a massive body, indeed a tiny acceleration will do, e.g. provided by ion drives or light sails.
On and around massive bodies you will have to "waste" a lot of force just to avoid falling into it as long as you are on a sub-orbital trajectory.
Another question: If we omit other planets, Sun etc., would the total gravitational force in the center of the earth be zero? The reasoning here is that there are equal masses in each direction of it. How about if we don't omit the other masses, were there still a point without gravitation somewhere near the center of the earth?
Yes.
Imagine there was no such point, you could construct a perpetual motion machine, creating energy from nothing. Not very practical on earth, but feasible on some sponge-like moons and asteroids in the outer solar system.
And third question, is there a measurable difference in the speed of things dropped at night and during the day, since in night the Sun also pulls the dropped item down, whereas in day it pulls it up? I tried to calculate the theoretical difference from the F= Gm1m2r-2 formula, but probably somehow screwed it up, since the 1N difference I got for 100 kg body sounds unbelievable.
You probably neglected that such an experiment happens in an accelerated frame of reference (earth orbiting the sun), which would cancel out most of the effect. What's left are higher order effects (see
tidal forces), which are much smaller than that.
I realize these are stupid and counterintuitive questions, but that's the reason they should IMO be asked. Besides, I'm a moron.
Naah, questions like that are actually asked as exercises in entry-level physics courses in universities, and unless you happen to imagine a suitable
Gedankenexperiment or do the correct math, the solutions are indeed not necessarily obvious.
By the way, you might be interested in
Kerbal Space Program, a really engaging rocketry simulator. Free demo available, and it's sale season at various gaming online stores at the moment.